Analysis and Approaches for IBDP Maths Ebook 2 | Page 236

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 73
1. Two players, A and B , alternately throw a fair six-sided dice, with A starting, until one
of them obtains a four or a five.
(a)
(b)
Find the probability that A obtains the first four or five in one of his first three
turns.
Find the probability that A obtains the first four or five.
[3]
[4]
2. Ted and Josh alternately throw a fair five-sided dice with one white face and four black
faces, with Ted starting, until one of them obtains a white face.
(a)
(b)
Find the probability that Ted obtains the first white face in his third turn.
Find the probability that Josh obtains the first white face.
[3]
[4]
3. A box contains four yellow balls and one purple ball. Chester and David play a game by
each taking it in turn to take a ball from the box, without replacement. The first player to
take a purple ball is the winner. Chester plays first.
(a) Find the probability that he wins.
[3]
The game is now changed so that the ball chosen is replaced after each turn. Chester still
plays first.
(b)
Find the probability that he wins.
[4]
4. Peter and Quinn play a game with a bag containing one red marble and three blue
marbles. Each player in turn randomly selects a marble from the bag, notes its colour and
replaces it. The first player to take a red marble is the winner. Quinn starts the game.
(a)
(b)
Find the probability that Quinn eventually wins.
The probability that Peter wins on his n th turn is
243
4096 . Find the value of n . [4]
[4]
226
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